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Department of Logic

Major Research Areas

The Department of Logic has a principal interest in basic theoretical research in logic, with applications in theoretical computer science, metamathematics and models of communication and social interaction. Our major research areas include: Metamathematics of Arithmetics (axiomatic theories containing arithmetics, their properties and interpretability, non-classical logics applicable in metamathematics such as intuitionistic and substructural logics); Set Theory (large cardinals and forcing, internal models, independence; links between forcing and the semantics of intuitionistic logic, set theory as a framework for building mathematics); Modal and Substructural Logics (coalgebraic logic, substructural logics, metamathematical properties of those logics and the use thereof in theoretical computer science, modal logics for modeling knowledge and information dynamics).

Profiling Projects

The department continually participates in the Czech Science Foundation projects.

Jonathan Verner is the principal investigator of Joint Lead-Agency research grant between the Austrian Science Foundation FWF and the Czech Science Foundation entitled Filters, Ultrafilters and Connections to Forcing (2017-2019).

Marta Bílková is the principal investigator on grant SEGA – “From shared attitudes to group agency” (2016-2018), Czech-German project Czech Science Foundation (GACR) – DFG 16-07954J

Radek Honzík is the principal investigator of Joint Lead-Agency research grant between the Austrian Science Foundation FWF and the Czech Science Foundation entitled The Continuum, Forcing, and Large Cardinals (2015-2017).

Over the past few years, Radek Honzík and Marta Bílková conducted their research under three-year postdoctoral projects supported by the Czech Science Foundation: in his project entitled The Continuum Function: Its Properties Relevant for Logic and Set Theory (2009-2011), Radek Honzík investigated the links between the continuum function and large cardinals; in her project entitled Proof Theory of Modal Coalgebraic Logic (2011-2013), Marta Bílková investigated modal languages – including classical modal logics – used to describe finite and infinite-state systems, their expressivity and formulations of proof systems for modal logics.

Major Publication Projects

The core of the department’s publication activity lies in individual publications in high-quality journals, a list of those is available at our website. The Department of Logic edits a series Miscellanea Logica, appearing since 2010 in the university-wide journal Acta Universitatis Carolinae – Philosophica et Historica and featuring articles by experts from various domestic and international institutions. The department’s other principal publication initiatives include the university textbook Logika: neúplnost, složitost a nutnost (Logic: Incompleteness, Complexity and Necessity) by the department’s Associate Professor Vítězslav Švejdar, published by Academia in 2002. The book has long been out of print, and a revised edition in English is currently in preparation. Another publication worth mentioning is a book targeted at talented secondary school students Logika pro všechny ochotné myslet (Logic for Willing Thinkers), written by Antonín Sochor, the department’s past member and lecturer, and published in 2011.

National and International Partner Institutions

The department’s leading national partners include a number of institutes of the Academy of Sciences of the Czech Republic, namely the Institute of Philosophy (Department of Logic and Department of Analytical Philosophy), the Institute of Mathematics (Department of Mathematical Logic and Theoretical Computer Science), and the Institute of Computer Science (Department of Theoretical Computer Science). The Academy of Sciences is the department’s principal partner in organizing academic projects, conventions and conferences as well as providing training opportunities for MA and PhD students. Internationally, the department enjoys several long-term partnerships in joint publications and mobility projects – members of the department have published joint publications with experts from the Institute for Logic, Language and Computation, University of Amsterdam, and from the Kurt Gödel Research Centre for Mathematical Logic in Vienna. The latter cooperation was in 2011-2017 partially supported by AKTION mobility projects.

Major Conferences and Events

In 2012-2017, members of the department participated in organizing the Winter School in Abstract Analysis, in particular the section “Set Theory & Topology”. In 2012, the department co-organised the international conference ALCOP (Algebra and Coalgebra meet Proof Theory). In the series of international LOGICA conferences organized by Institute of Philosophy of the Academy of Sciences, members of the department often appear as members of PC, editors of the proceedings and speakers. In February 2010, the Department of Logic co-organized the international conference Beauty of Logic II, held to mark the 70th birthday of Petr Hájek, a leading Czech logician; and consequently a series of meetings, Prague Gathering of Logicians, held annually in 2013-2017, bringing together logicians from various Czech and international institutions. Most recently, the department is organizing a major event in nonclassical logics TACL 2017, and in 2019 we will participate in organization of a major event in logic and philosophy of science, the Congres CLMPS. Furthermore, the department runs a regular research seminar bringing together the department’s academic staff and students in the PhD programme, which is also open to excellent MA students